In the given figure,a solid cylinder of mass $m_2$ and radius $R$ is suspended by a string wrapped around it,which passes over a fixed pulley of mass $m_1$ and radius $R$. If the linear acceleration of the solid cylinder is $a_2$ and there is no slipping,what is its angular acceleration $\alpha_2$?

$A$ small particle of mass $m$ is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius $a$. All motion occurs essentially in the horizontal plane. If the angular velocity of the cord is $\omega_0$ when the distance from the particle to the tangency point is $r_0$,then the angular velocity of the cord $\omega$ after it has turned through an angle $\theta$ is

In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. If there is no slipping,find its angular acceleration $\alpha_2$.

$A$ mass $m$ is supported by a massless string wound around a uniform cylinder of mass $M$ and radius $R$. On releasing the mass from rest,it will fall with an acceleration of:

Between the hour hand of a clock and the rotation of the Earth about its own axis,which has a lower angular speed?

Explain the definitions of angular position,angular displacement,and angular speed for the motion of a rigid body.